What is (\partial)/(\partial x)(t^2e^{(x^2)/(2t)}) ?

The answer to (\partial)/(\partial x)(t^2e^{(x^2)/(2t)}) is e^{(x^2)/(2t)}tx

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(\partial)/(\partial x)(t^2e^{(x^2)/(2t)})

\frac{\partial}{\partial x} (t^{2} e^{\frac{x ^{2}}{2 t}})

e^{\frac{x ^{2}}{2 t}} t x

Solution steps

\frac{\partial}{\partial x} (t^{2} e^{\frac{x ^{2}}{2 t}})

Treat

t

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= t^{2} \frac{\partial}{\partial x} (e^{\frac{x ^{2}}{2 t}})

Apply the chain rule:

e^{\frac{x ^{2}}{2 t}} \frac{\partial}{\partial x} (\frac{x ^{2}}{2 t})

= e^{\frac{x ^{2}}{2 t}} \frac{\partial}{\partial x} (\frac{x ^{2}}{2 t})

\frac{\partial}{\partial x} (\frac{x ^{2}}{2 t}) = \frac{x}{t}

= t^{2} e^{\frac{x ^{2}}{2 t}} \frac{x}{t}

Simplify

t^{2} e^{\frac{x ^{2}}{2 t}} \frac{x}{t} : e^{\frac{x ^{2}}{2 t}} t x

= e^{\frac{x ^{2}}{2 t}} t x

- x, - 10 x + 14, x = 0

x^{3} e^{2 x}

n = 0 \sum \infty \frac{x ^{n}}{3 \cdot n}

y = \frac{3}{x}

\frac{d}{d t} (\frac{1}{2 t ^{2} + 1})

What is (\partial)/(\partial x)(t^2e^{(x^2)/(2t)}) ?
The answer to (\partial)/(\partial x)(t^2e^{(x^2)/(2t)}) is e^{(x^2)/(2t)}tx